I use nut files, so cut down rather than sand the bottom of the nut, and I also cut down using my eye and experience as to the right height (and often cut too low so I've got a good stock of spare nuts). But I'd use feeler gauges to measure the height of the first fret, and add 0.4mm on top of that. The base of the nut needs to be sanded down so the nut slots are that distance from the fretboard. Just use the two E string slots, the rest will take care of themselves.

That will give you a reasonable string height over the first fret, but you can probably go a bit lower if you want. But don't take it lower before you've got the action and neck relief sorted out.

As to the bridge height, what sort of neck relief is there? I'd start off with the neck set flat, as string tension will add some bow to it, raising the strings up slightly.

Are the body neck screw holes big enough to just pass the screws through without them binding on the sides and needing screwing down? They should only screw into the neck itself in order to fully pull the neck flat into the bottom of the pocket. If you have to screw through the body and neck, there's a good chance that the screw can't turn further because its all the way into the body, but there's still a gap between the neck and the body. This gap will change the neck angle and if it's at the body end of the pocket, will raise the neck angle requiring a higher bridge position.

Also check for any splinters or other small objects in the neck pocket. It doesn't take much for the neck not to sit flat and change its angle.

Once you get the neck flat and it seated properly in the pocket, then run a long metal straight edge along the neck and see how much height there is between it and the body at the bridge position. A photo of the bridge alongside a ruler would be nice to get an idea of how tall it is.

As has been said by others, the 2-point bridges are a bit different to the vintage 6-screw types, and the bridge plate does sit a bit off the body, allowing it to float. But maybe 2-3mm rather than 5mm off. But you can also raise the individual saddle heights as well.

If the neck angle is very wrong and the bridge needs to go very high, then the options are 1) put a shim under at the neck end of the pocket (easy to do) or 2) modify the pocket or the neck heel to adjust its angle (harder). I'd always suggest doing 1) first to work out how big an increase or decrease in angle you need. I normally use a 10mm x neck width piece of veneer as a shim, though any hard material will do. A shim at the body end of the pocket is invisible, but any sizeable shim at the neck end of the pocket will be visible, so you may want to think about altering the heel angle or pocket floor angle instead.

Just realise that a small shim has a much larger effect on the neck angle than you may think. Depending on the neck pocket length it's between a 4:1 or 5:1 increase, so a 0.5mm shim can lower (or raise) the string height at the bridge by 2mm-2.5mm.